Ocean bio Emojis & Symbols

⠀⠀⠀⠀⠀⢀⠀⣶⠄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣦⠀⢀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⣀⠀⠀⠐⠁⠌⠀⠀⠀⠀⡠⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠀⠀⢀⠀⠀⣰⣋⣠⣤⣶⣿⣷⣶⣤⣤⣤⣶⣶⣿⣿⠃⠀⠀⠁
⠀⠋⠀⠀⠓⠘⠀⠀⠀⠀⢰⢇⡏⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢨⡇⣿⣿⡇⠀⠀⠀⠀⠘⠛⠋⠁⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡿
⠀⠀⠀⠀⠉⠀⠀⢀⣾⣿⡿⢸⡇⣿⣿⣿⢀⠃⠀⠀⠀⢀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⢸⢳⣿⣿⡿⢊⡀⠀⠀⣀⢀⡀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⠀⢠⡟⠉
⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠬⢿⣿⠋⠀⣼⠛⠀⣟⣁⣤⠆⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⠃
⠀⡠⠀⠀⠀⠲⣶⣄⣀⣐⣅⣀⣀⣦⣤⣴⣾⣷⣿⣿⡿⠁⠀⠀⠀⣶⣶⣄⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣦⣀⣀⣀⣴⡿⠋⠐
⠀⠁⠀⠀⠀⠀⠘⣿⡿⢿⣿⡿⢿⡿⢿⣿⢿⣿⡿⠏⠀⠀⠀⠀⠀⠈⠙⢿⣆⡄⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠀⠙⠋⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⡻⠀⣀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠸⢷⣆⢡⡾⠟⠁⠀⢀⠀⠀⠀⠄⠀⠤⠀⠀⠀⠠⠀⢀⣠⣤⣾
⠀⠀⣰⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠷⠰⠇⠀⠀⠙⡾⠁⠀⠀⠀⠊⠀⠀⠀⣀⠀⠐⠐⠂⠉⠀⢠⣿⢿⣿⠏
⠀⠈⠃⠀⢠⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⡒⠶⠤⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠠⠐⡆⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⣦⡀⠀⣀⣀⡀⠀⠀⠀⢀⣠⣶⣶⡆
⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠢⠚⡀⠀⠀⣰⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣷⡀⢿⣿⣿⣷⣄⣠⣿⣿⣿⣿⠃
⠀⠀⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠑⢤⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣷⡈⠻⣿⣿⣿⣿⣿⡿⠛⠁
⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠑⡤⢼⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣷⡄⠀⠈⣹⣿⠁
⠀⠀⠂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢤⡀⠀⠉⠁⠀⠀⠈⠛⠉⠀⠀⠈⠛⠛⠉⠀⠙⠿⠿⠛⠐⢿⡿⠟⠀⠀⠠⠄
⠀⣤⣀⣀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣯⣇⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⡀
⠀⠸⣟⣿⣿⣄⠀⠙⠿⢿⣿⠿⣿⣿⣿⣀⣀⣤⣾⣿⡿⠁⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⡄⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠛⠿⠿⢦⣴⠀⠀⢻⣇⣼⣿⣿⣿⣿⣿⣿⣫⣥⣶⡿⠃⠀⠀⠀⢀⣴⠟⠋⠉⠉⢿⣿⡿⠿⠛⠀⠀⢷⣄⣹⣯⣿⡯⠋
⠀⠀⠀⠀⣀⣤⣤⣥⣀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠛⣿⠟⣿⣷⣤⠖⠀⠨
⠀⠀⠀⠘⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡻⣿⣿⣟⠿⠿⠾⠿⠛⢋⣴⠾⠛⠛⠛⢶⣶⣶⣿⣿⡿⠋⠀⠀⠀⠁⠉⠉⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⣫⣿⡿⠃⠈⠻⣮⣝⣛⠋⠀⣀⣤⡾⠋⢁⣠⡇⠀⠀⠈⠻⠿⠟⠁⠀⠀⠐⢀⠀⠀⢀⣤⣶⣦⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠀⠀⠀⠀⠈⠙⠻⠿⠟⠛⠁⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠂⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣂⣶⠖⠷⠶⠞⠻⢝⠲⣿⣦⣦⣤⣶⣄⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⡷⠞⠋⠉⠉⠉⠒⠢⢄⠀⠀⠀⠘⠻⣟⠀⠹⣟⢷⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣾⣿⣧⢤⣤⣀⠀⠀⢀⡀⠀⠀⠑⠀⠀⠀⢀⠘⠄⠀⢹⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣵⣟⣃⠤⠄⠀⠀⠀⠀⠀⠀⢉⣦⡀⠀⠀⠀⠀⠈⠃⠀⠀⢦⢣⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡞⠉⡀⠄⠀⠀⠀⠀⡀⠲⡀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣮⢂⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⢎⡴⠊⢀⠄⠀⠀⠀⠲⣾⣷⡌⠆⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⣰⢸⣿⢦⠻⣟⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⡟⡔⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⢰⠀⠀⠀⣿⠂⢰⠀⢀⠀⣶⡏⣰⣿⢷⣷⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⡶⡟⢰⠇⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⡿⢀⠀⠀⣿⢀⣾⠀⠎⣰⠟⠋⠁⣀⠤⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠏⣇⡜⠀⠀⠀⠀⠀⠀⠀⡸⣿⠏⣾⡇⡈⠀⣸⠃⣰⠇⣸⣞⠅⠀⠀⡨⠔⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣄⠟⠁⠀⠀⠀⠀⠀⣠⡶⠙⠋⢠⡟⡰⠁⠸⠃⣴⣯⣾⠟⠁⠀⡠⠊⠐⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⣠⣶⣏⣼⠁⠀⣶⣾⡿⠟⡁⠀⣰⠊⠴⢊⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⡽⠏⠀⣠⣾⢟⡽⠛⣁⣴⡿⠟⠉⠀⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢋⡉⠀⠀⣉⣤⣴⡿⠛⢋⣡⡴⠿⠛⠉⠀⠀⢀⡠⢊⣥⠖
⠀⠀⠀⠠⢴⣷⣦⣤⠵⠖⠲⣞⣩⣿⣭⡶⠞⣫⠥⢖⡠⠀⠀⠀⢀⡥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠋⣋⠩⠂⠚⠉⠀⠀⠈⢀⠀⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠛⠟⠛⠒⠒⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⢎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⡀
⠀⢀⠀⠀⠉⠒⠠⡬⣍⣉⢤⠀⠀⠀⠀⠀⠘⡌⢦⡙⢲⢤⣀⣀⣀⣠⡞⠋⣰⠏⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣰⡟⠉⠈⠉⠢⠀⠈⠐⢆
⠀⣼⠀⢠⠀⠀⠀⠲⠄⢄⠠⠆⠀⠀⠀⠀⠀⠹⣆⠹⣦⡀⠒⠋⠛⠀⠀⣴⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⣿⡄⠈⠦⠴⠀⠈⢓⡀⠀⠠⢄
⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⡀⠐⢄⠀⠀⠀⠀⠀⢻⢠⠈⠻⣄⡀⠀⢀⡾⠁⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠑⠀⠀⠀⠐⠀⠈⣿⡄⠀⠘⠄
⠀⠸⠀⠋⠀⡜⠀⠠⡶⡚⢡⠄⡈⠀⠀⠀⠀⠀⣸⠸⠀⠀⠈⢻⣤⣞⠁⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠻
⠀⠀⠃⠀⠀⠀⣴⣢⣿⣽⠋⠀⠀⠀⠀⠀⠀⣴⠇⠀⢀⣤⠴⠛⢻⡏⠛⠳⠶⠦⠤⢤⣤⣀⣀⣉⡙⠂⠀⠀⠈⠢⣀⠐⠄⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠘⠀⠐⠐⣿⣿⡿⠎⠁⠀⠊⠀⢀⡰⠚⡡⠴⠚⠉⠀⠀⠀⠈⣧⠀⢀⠄⠀⣐⣠⡤⠴⠶⠒⠂⠀⠀⠀⠀⠀⠈⠙⠒⢒⣶⣤⣴⣾⠟⠛⠁
⠀⠀⠀⡅⠀⢰⡿⠋⠀⢀⡴⠁⠀⠐⠁⣀⡡⠤⠶⠖⠶⢤⡀⡀⠀⢻⠀⢠⣪⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠺⠇⢸⠀⠈⠘⢯⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⡻⠁⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠀⢸⡄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠎⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠹⡀⠀⡤⠂
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠊
⠀⢰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⣦⠑⢠⠇⠀⠀⠠⠂⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠁⠆⠈⢠⠀⠐
⠀⠀⠂⠀⠀⡄⠀⠀⠀⠓⠀⠉⠀⠀⠀⠀⠀⠠⣄⢀⡀⠋⠀⠁⣀⠉⠘⢃⡀⢘⢂⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢠⠂⠀⠀⠀⠀⠂⠀⠐
⠀⢀⠛⠂⠄⢁⢀⠀⡀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠛⠁⡄⠘⠋⢈⠁⠁⣀⣤⠀⠄⠀⠐⠀⠀⠀⠀⠀⣦⠀⠂
⠀⠂⠀⢀⠒⠀⠀⠆⣄⠀⠉⢱⢤⠀⠠⠀⠀⠘⠀⠤⡽⠀⠀⠐⠈⢨⠂⠀⢀⠀⠱⠚⠅⠠⠄⢄⠀⠐⠘⠀⠀⠀⠀⢸⠢⡁⠀⠠⡆⠀⢰⠁⠀⠀⠰⠁
⠀⠅⠀⠐⠀⠂⠠⠀⠀⠀⠒⠀⠀⡁⠄⠂⠉⠉⠀⠀⢤⠄⠠⡴⠀⢠⠏⠀⠤⠀⠐⠀⠠⠀⠑⠀⠂⠀⠠⠀⠀⠰⠄⠀⠄⠈⢤⡃⠠⠀⠘
⠄⠀⠂⠀⠈⠀⠀⣀⠤⢀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡠⠂⠄⠠⡆⠀⢀⠉⠀⢠⠀⠀⠀⠀⣼⡄⠀⠀⠀⢀⠀⠄⠀⠘⠧⠠⠀⠅⠀⠀⠀⠀⡁
⠀⠀⠀⠀⡂⠀⠄⠀⠀⠀⠉⠀⠠⠀⠂⠀⠀⠀⠀⠀⠂⠈⠁⠑⠘⠇⠰⠇⠀⠀⠀⠄⠀⠁⡆⠀⠀⠀⠀⠀⠀⢃⠀⠠⠀⠀⠠⠁⠩⡔⠀⠀⠀⢀⠀⠃⢈
⠀⠀⠀⠲⠐⠂⠀⠀⠀⢀⠂⢀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡑⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⠉⠲⡉⠀⣉⡈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⡄⠀⠀⠀⠀⢾⡀⠀⠀⢀⣠⣃
⠀⠀⠀⠀⠐⠂⠢⡀⠒⢁⠀⠲⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠢⡀⠄⠀⠐⠑⡘⢀⡄⠀⠈⠁⠆
⠀⠀⠀⠀⠁⠒⣀⣀⠀⠘⠀⠀⠙⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡑⢀⣷⢼⠆⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡙⡞⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣅⣩⣚⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠿⠿⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣖⣒⣲⣶⠷⠿⠿⢿⣷⣶⣦⣍⡛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠿⠿⠿⣯⡽⠿⠿⣷⣶⣤⣍⡙⠻⢿⣷⣦⡙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠽⣗⣚⣛⣿⣛⣛⠛⣲⣾⠷⠶⢤⣭⣝⣿⣛⠳⠦⠬⣽⣿⣷⡌⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣟⣙⣛⡓⣲⢸⣿⠀⠙⢿⣿⣶⣄⡀⠉⠙⠻⢿⣷⣶⣤⣀⠉⠛⠿⣶⣬⡙⢦⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣗⡒⠶⢤⣉⠉⣧⠈⢿⣷⡄⠀⠉⠻⣿⣿⣶⣄⡀⠀⠈⠙⠿⣿⣿⣦⣄⠀⠙⢿⣦⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠭⡓⠦⣈⢣⠹⣦⠀⠻⣿⣦⣄⠀⠀⠙⠿⣿⣿⣶⣄⡀⠀⠈⠙⠿⣿⣷⣄⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⣠⢟⡄⠑⠠⠁⠣⡘⢷⣄⠈⠛⢿⣷⣄⡀⠀⠈⠙⠿⣿⣿⣦⣄⠀⠀⠈⢻⣿⡆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠝⠷⠾⠋⠵⣻⡯⡃⣄⠀⠀⠈⠲⢌⠳⢦⣀⠉⠛⠿⣶⣤⣀⠀⠈⠙⠻⢿⣷⣤⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡄⢰⠚⠒⠒⠚⣋⣡⠞⣱⢁⠀⠀⠀⠀⠀⠈⠀⠨⠙⠒⠤⠄⢉⠛⠛⢶⡦⠄⢤⡈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇⡴⠚⠛⠉⢀⡴⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⢍⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧⠸⡀⠀⠠⠞⢉⠄⢈⡄⠁⣤⠀⠰⣄⡀⠢⠄⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⢀⡄⠀⣰⡇⠀⢸⣆⠀⠘⠷⣄⡀⠉⠓⠶⠤⣤⣍⣩⠥⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⡞⠁⠀⠀⠀⠀⣅⠀⢸⣇⠀⠹⣷⡀⠀⠙⢷⣤⣀⠈⠙⠓⠶⠦⣤⣤⡤⠴⠒⣁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠘⠜⣄⠀⠐⠀⢠⣄⠹⢦⡀⠙⢷⣄⡈⠛⠷⣤⣀⡈⠙⠛⠶⠶⠤⠤⢴⣖⣒⣋⡭⠭⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠴⠷⢮⣝⣲⣭⣓⣲⣬⣝⣓⣲⠦⣭⣭⣝⣛⣻⣿⣯⣽⣭⡭⣟⣶⠯⠃⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⡿⠿⠿⠿⠟⢳⡈⠩⢔⠄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡈⠁⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠁



⣶⡖⢲⡶⣶⣶⡶⡶⢶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣷⣶⣶⣶⣜⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠅⠄
⠀⢀⣠⣤⣶⣶⣾⣿⣿⣟⡩⠩⠉⠁⠀⠉⠹⠉⠘⠒⠸⠪⠀⠂⠶⠀⠩⠭⠍⠛⠿⢙⠋⠟⡻⠷⠶⢶⣷⣶⣬⣀⣀⣤⣤⣴⣾⣿⣿⡿⠖⠂⠘
⠚⠛⠛⠛⠗⠁⠀⠈⠀⠉⢧⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠁⠀⠀⠀⠘⠀⠁⠈⠀⢈⠉⠉⠉⠠⠁⣘⣿⣃⡀
⠆⠀⢐⣌⠂⠀⠀⠀⠄⠀⣸⢈⡠⠔⠛⠒⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠑⠂⠀⠀⠡⣤⡦⢾⣦⣤⣤⠦⠤⢄⣠⢤⣤⣤⣤⣦⣤⣶⣿⣿⣦⡤⢤
⠀⠀⠀⠀⣀⣄⠀⠊⣠⡾⣿⣿⡒⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⠉⠀⠀⠉⠛⢿⣿⣷⡯⠭⢽
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⢬⣍⣉⣉⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠤⠔⠺⠆⠀⠀⠀⠩⣼⢤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠙⠿⣿⠷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠹⣏⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠹⡂⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢠⠐⠂⢂⠘⢆⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⣤⡤⣀⠀⠀⠁⢸⠀⠀⠋⠠⠙⠂⠐⠁⠀⠂⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠀⠀⢀
⠉⠁⢈⢳⡄⠐⠋⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠤⠀⠘⠀⣄⢤⣤⠞⠇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣐⡃⣢⡾⠧⣤⡤⣤⢀⣀⠀⢀⠅⡒⢋⡛⢆⠀⣡⡴⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂⠀⠀⠀⠀⠀⠀⢧⡀⠄⠀⠀⠀⠘⠋⠀⠀⠀⠀⢀⡤⠂⠀⠀⠘
⠉⠉⠉⠀⠀⠸⣜⡐⢾⢻⡿⠛⠀⠂⠶⠀⠀⠃⠉⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⡃⠀⠀⢆⢠⠁⠮⠀⠄⠀⠈⠀⠀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠐⠀⢀⠀⠀⣐⠀⠙⢀⡢⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠸⢷⡄
⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⠦⠄⣀⣂⣰⠐⠋⠀⠀⠈⠁⠡⠌⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠢
⡀⡀⢀⣀⠀⠑⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠉⠈⠑⠲⡶⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⢠⣮⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⢤⡄⡀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚
⢀⣶⣲⡐⣢⠤⣄⣀⡻⣀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠶⢤⣠⡄⠀⠐⠀⠀⠀⠀⠀⠀⡆⠠⠀⣈⡶⠒⠲⣄⠀⠀⢠⡄⢀⢤⠀⠒⠀⠀⣤⠀⠛
⠀⠁⠒⠈⠁⢀⣠⡴⢹⠛⠺⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢢⠀⠰⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠸⣏⠀⣠⣑⣤⣦⣼⠿⠀⠁⠀⠄⠀⠀⠀⠈⠁⠢
⠐⠂⢐⠛⠻⠭⠛⠥⠃⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⡏⠆⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⠁⠀⠀⠀⣈⠋⠉⠻⢼⠂⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⢁⠼⢿⡀⠀⠀⠀⡷⡶⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠻⠳⠠
⠀⠀⠀⠀⠀⠀⡠⢤⢀⣀⢀⠄⠂⡄⢂⡐⠁⠀⠀⠀⣀⢀⡼⢃⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠐⠀⠀⢂⡀⠠⠀⠈
⣤⣤⣾⣥⣍⣈⡋⠀⠀⠀⠀⠀⠁⡀⠂⠀⠀⠀⠀⣶⠿⠋⡠⠎⠀⠀⠀⠀⠀⠀⠀⣶⠀⠂⠀⠀⠈⠁⠉⠁⠉⠀⠀⢀⣤⠰⠆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠤
⠈⠁⠸⠀⠀⠘⠣⣤⠀⡤⠄⢴⠛⠀⠀⠀⠀⠀⠐⠛⢀⡉⠦⠔⠀⠀⠀⠀⠠⠀⠩⠘⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠉⣄
⢀⠠⠇⢀⠀⠀⠀⢒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠐⠀⠀⢀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠘⣿⡷⠤⠀⠀⡋
⣶⠆⠰⠁⠀⡠⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠐⠂⠀⠀⠀⠀⠐⢀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢹⣀⠃⠀⠐⠀⠀⠀⠀⠀⠞
⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠐⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠂⢠⣀⣀⠀⠄⠀⠀⡀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠈⠔⠂⠀⠀⠃
⠀⠀⢄⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢰⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠆⠀⠀⢠⣀⡀⡀
⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⣷⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⡌⢠⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⡾⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⢿⣿⠃⠀⢀⠸
⠀⠀⠀⠀⢀⠘⢠⠄⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠳⡘⠧⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠄⠀⠁⠀⠉⠀⠀⣴
⠀⠀⠀⠀⠎⠠⠀⠖⠀⢀⠀⠀⠀⠀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⠁⡀⢠⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠀⣀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠄⠰⡀⠠⣈⠃⡇⠐⢠⠤⠊⠉⠃⠀⠀⠫⠲⠛⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠋⢀⡤⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠐⠠⣀⠀⠀⠀⠀⠀⠀⠈⠆⠉⠢⢄⠴⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠒⠈⠂⠐⢀⠀⠀⠀⠀⠀⠀⠀⠔⣠⠠⠤
⣀⡀⠀⠸⠆⢀⠀⡀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢁⡀⠀⠀⢄⣀⠤⣇⣀⠀⠀⠀⣀⢀⠏⠁⢀⣀
⠈⠁⠀⠀⠀⠉⠀⠀⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡀⠀⠀⠚⠀⠀⠀⠀⢀⡏⠀⠀⠣⠖⠛⡏⣄⣀⠉
⠡⠈⠀⠀⠀⠀⠀⠀⢄⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠙⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⣲⣿⠿⢛⣿⡿⠟⣛⣿⣿⠿⠛⣛⣛⣛⣿⣿⣿⣿⣻⣿⣿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⣩⣶⠟⢋⣤⡾⠟⣉⣴⡾⠟⢋⣤⣶⠿⠟⣋⣩⣤⣴⡶⠶⠶⠶⠶⠾⠿⢭⣽⣓⠶⣖⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⡾⢋⣥⠾⢛⣩⡴⢞⣋⡥⠶⣛⣫⡭⠴⣒⣛⣭⠭⠴⣶⣒⣚⣛⡛⠛⢛⡿⣖⢀⡿⣅⢿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢞⡡⣺⠏⣴⢪⡝⢰⠊⡽⠒⠩⠟⢋⡩⠥⠤⠀⠤⠤⠜⣓⠢⠌⡓⢭⡓⢌⠢⣑⢮⡳⡝⢎⢣⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⢁⡼⠁⣴⠋⢠⡏⠀⣿⠀⢹⡆⠘⣧⠈⢳⠀⠑⣦⠈⢳⡄⠀⢲⠏⠀⠈⣁⡈⠂⠙⠊⠣⠑⠌⢮⠳⡹⡜⢆
⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠏⢠⡟⠀⣼⠃⣠⠟⢀⡼⠃⣠⠏⢀⠼⢁⡠⠋⡠⠞⠁⠴⠋⠀⠔⠋⠀⠐⠋⠁⠀⠠⢤⠀⠀⠀⠀⢈⠣⠱⡘⡌⢆
⠀⠀⠀⠀⠀⠀⠀⠙⠆⠸⠄⠸⠁⡼⠁⠔⠁⠔⡋⡀⠊⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠃⢡⢰⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢆⠀⡇⠐⡇⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡠⠃⡄⠀⡄⠘⡄⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠠⠂⠄⡄⡐⡠⢡⢂⠆⡌⡈⡸
⠀⠀⠀⠀⠀⣾⠀⣾⠀⢸⡅⠘⣇⠀⢷⡀⠙⣆⠈⠳⣄⠙⢦⡈⠑⢤⡀⠒⢤⡀⠂⢤⣀⠐⠠⢄⣀⠐⠀⠠⠤⠤⠜⠂⠀⣠⠁⡄⢈⠈⠰⢡⠃
⠀⠀⠀⠀⠀⠘⠳⣌⠳⢄⡙⢦⡈⠳⣄⠹⢦⡈⠳⣄⠘⢧⡀⠙⣦⠀⠙⣦⠀⠙⣦⡀⠈⠳⣦⣀⠈⠉⠓⠒⠒⡒⠒⡈⢉⠀⡪⢠⢅⡞⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⡺⣍⢦⡙⣆⢨⡓⢤⡛⢤⣘⠧⣄⣛⡢⠤⠬⠯⠤⠤⢔⣚⡩⠤⣚⠥⣚⡵⣪⢕⡫⢚⠵⣣⢊⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣝⡳⠯⣝⣛⠷⣿⣛⡲⠯⣽⣓⠾⠭⣿⣛⣻⠤⠾⣿⣔⣋⣁⣫⣵⡋⠶⣥⢊⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣬⡙⠿⣶⣍⡛⠷⣦⣭⡙⠻⢶⣬⣍⣛⠻⠶⠶⣦⣭⣭⡭⠤⢶⣛⣥⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣌⠻⣿⣦⣈⣻⣿⣷⣤⣍⣛⣿⣿⣿⣖⣲⡶⠾⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⢭⣟⡛⣟⣟⡛⣛⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠠⣦⡀⠀⠀⠀⠀⠀⢰⣾⣦
⠀⠀⠀⠀⠀⠙⣿⡷⠀⠀⠀⠀⠀⢙⡿⢷⣶⣦⡄⠀⠀⠀⠄⣹⣾⣿⣶⠡⠀⠀⠀⠀⢰⣬⣿⣯⢔
⠀⠀⠀⠀⠀⠀⣝⠁⠀⠀⠀⠀⠀⠀⠁⠰⠧⠿⠃⠀⠀⠀⠀⠀⠉⠉⠑⠁⠀⠀⠀⠀⠀⠙⠋⠻⠁
⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢀⣴⣠⡉⣉⠁⠀⠀⠀⠀⢀⣠⣶⣦⣄⠀⠀⠀⠀⡾⢻⠜⡩⢻⡆⠀⠀⠀⡀⣾⢖⣶⣆⡀
⠀⠀⠀⠐⠋⣿⣿⢇⠻⠀⠀⠀⠀⠒⠛⠟⠻⠿⠛⠁⠀⠀⠀⠙⣷⣷⣷⠟⠁⠀⠀⠈⠓⣿⠀⢿⠟⠋
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣰⣶⣤⣄⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠁⠰⠘⠯⠛⣆⠀⠀⠀⠀⠀⠼⣿⡟⠤⠀⠀⠐⠚⢷⣶⣾⡏⡅
⠀⠀⠀⠀⠉⠉⠛⢇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠼⠦⠀⠀⠀⠀⠀⠋⠉⠢⠀⠀⠀⠀⠀⠘⠉⠀⠁


⠀⠀⠀⠀⠀⠠⡤⣝⠀⣄⠀⠀⠀⠀⠀⢀⣧⠀⢀⠀⠀⠀⠀⠀⣶⡶⠖⠒⠂⠀⠀⠀⢺⡇⣀⢸⡷
⠀⠀⠀⠀⠠⠐⠻⣦⠌⠀⠀⠀⠀⠈⠛⣿⣿⡟⠋⠀⠀⠀⠀⠂⡠⠒⠀⠀⠀⠀⠀⠀⠀⢹⣿⡎
⠀⠀⠀⠀⠠⠾⠾⠧⠤⠀⠀⠀⠀⠀⠰⠋⠉⠻⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣷⣾⣿⣦⣀⡀⠀⠀⢀⠞⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣻⣛⣵⠶⢶⡹⣮⣙⡛⠿⢷⣦⡾⣿⣿⣦⡀⠹⡟⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣒⡿⢋⣥⡾⡽⣫⣴⣶⣶⣅⣉⠛⠻⢿⡶⠁⠀⠀⠈⠻⣷⡄⢹⣶⣄⡈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣩⣤⣭⣟⣩⣜⡴⢋⣤⣶⣦⡝⢿⣿⠿⠶⣀⣀⠀⠀⠀⠀⠹⣿⡀⠉⠻⢿⣦⡀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⡞⠉⣠⣤⣌⣋⡼⣱⠟⣉⣤⣤⡙⣎⠛⢓⣠⢿⣿⣷⣄⠀⠀⠀⠘⣷⠀⠀⠀⠻⣿⣆⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢠⠏⣠⢞⣩⣭⣍⡻⣽⢃⡾⠋⢉⣉⠙⢾⣋⡉⠁⠀⠙⢿⣿⣆⠀⠀⠀⢹⡎⣷⡀⠀⠈⢿⣧⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⣾⠎⡰⠁⠁⢀⣀⣈⠻⣦⠟⣠⠾⠛⠛⠛⣀⠉⢻⡆⠀⠀⠈⢿⣿⣆⠀⠀⠀⣷⠹⣿⣄⠀⠀⢻⣧⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⠟⠈⠀⠀⠠⠖⢁⡠⠴⠄⠘⣰⠃⣤⠾⠛⡇⠙⣧⠀⢿⠀⠀⠀⠈⢿⣿⡄⠀⠀⢸⡄⠘⣿⡄⠀⠀⢻⣧⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⡿⠁⣰⠀⠀⠐⢀⠔⠉⠀⡠⠄⠄⠃⠞⢁⣴⠶⠉⡄⠘⣧⢸⡇⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢿⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣴⠟⢀⡾⠃⠀⠀⠠⠃⠀⡴⠋⠀⢀⠄⠀⠀⠛⣩⡆⠀⠘⡄⠘⠀⣿⡀⠀⠀⠀⠈⣿⣧⠀⠀⡄⠀⠀⢹⣷⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣼⠋⢠⡟⠁⡀⠀⠐⠁⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠸⣧⠀⠀⠀⠀⠘⣿⡆⠀⢸⠀⠀⠀⢿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡾⠁⣠⠏⢀⡾⠃⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠡⠀⠀⢿⡆⠀⠀⠀⠀⢹⣿⠀⢸⡇⠀⠀⠸⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡼⠁⣰⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢿⡆⠀⢿⠀⠀⠀⣿⠀⠀⣼⠀⠰
⠀⠀⠀⠀⠀⠀⢀⡟⠀⣼⠃⢰⠏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⡿⠀⢀⠏⠀⠁
⠀⠀⠀⠀⠀⠀⣼⠁⢰⠇⢀⡏⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⣿⠀⢸⡇⠀⢰⠇⠀⠀⡆
⠀⠀⠀⠀⠀⢠⡇⠀⡟⠀⡸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣀⡠⠤⠆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠘⠀⠘⠀⡄⠀⢸⠀⢀⡇
⠀⠀⠀⠀⠀⢸⠁⢰⡇⠀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣀⣀⣀⣤⠤⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢠⡇⠀⡿⠀⢸⠃
⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢀⠀⠈⠉⠉⠉⠉⠉⣉⣀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢰⡇⠀⡟
⠀⠀⠀⠀⠀⠘⡆⢸⡆⠸⡀⢸⠀⠀⠀⡀⠰⠀⠀⠀⠘⡀⠀⠀⠀⠔⣡⠞⠙⠛⠛⠛⠛⠉⠉⣉⣀⣤⣤⠢⣤⡀⠀⠀⠀⠀⠄⡀⠀⠀⠏⠀⡾⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠹⣄⠳⡀⠣⡀⠃⠀⠀⣬⡰⢤⡀⠀⠀⠈⣠⡴⠾⠟⠁⠐⠛⠛⠛⠛⠛⠛⠋⠉⣉⣀⣤⡄⠀⣀⣰⠂⡄⠀⣠⠇⡆⠀⠀⡼⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠓⠲⢦⡐⡿⢮⡛⢦⡄⠀⠙⠳⠦⢤⠤⠔⠂⠐⠓⠶⠶⠖⠛⠛⠛⠛⢉⣉⣠⣤⠤⢌⣩⠴⠃⣠⡤⠞⣱⠀⡼⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣬⠟⢈⠦⡿⠂⠉⢶⣦⣤⣤⡤⠤⢀⢈⣤⣤⣀⣀⣀⣀⣀⣛⣛⣛⣉⣡⣤⣾⣷⡖⠲⠞⢡⣞⡩⢵⣈⠴⠋
⠀⠀⠀⠀⠀⠀⣴⣾⡏⣿⡁⠺⣿⡄⡇⠸⣧⡀⠀⠀⠀⠀⢀⣠⡶⠃⠊⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⣀⣀⣤⣾⣿⡿⠀⢹⣦⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣬⡻⢦⣌⣑⣽⣦⡙⠻⠷⣶⣶⡾⠟⠉⡰⣱⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠟⠛⣉⣡⣤⠶⣟⣥⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠿⠿⠿⠿⣿⣶⣤⣤⣤⢴⣊⣴⣦⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⡤⠴⣶⣶⠶⣛⣿⣿⠏⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣭⣿⣶⣶⣬⣭⣭⣿⣿⣯⣭⣭⣭⣥⠶⣾⣛⣯⣷⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣶⣶⣾⣶⣶⣶⣾⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⢀⠀⣀⣀⢀⡀⢀⡀⢀⣀⢀⡀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⠀⣀⣀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠤⠤⠤⠤⠴⡇⢸⠀⠈⠁⠈⠓⠶⠞⠉⠈⠙⠲⠖⠋⠁⠉⠳⠶⠚⠁⠈⠓⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡀⠤⠤⠤⢰⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠳⡄⠀⣠⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣬⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡁⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠙⢦⡙⢦⡀⠀⠀⠀⣠⣤⣤⣀⢀⣠⠾⢿⣿⣿⣿⣿⣿⠿⢦⣄⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠋⠀⠳⡄⢳⡀⠀⣾⣿⣿⣿⣿⣯⠀⠀⠀⠉⢹⡋⠉⠀⠀⠀⢨⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠶⠶⠶⢹⡄⢷⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠶⠦⠶⠦⠴⡇⢸⠀⠀⠙⠛⠛⠋⠀⠀⠀⢀⣀⣈⣁⣀⠀⠀⠀⠀⠛⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡄⠤⠤⠤⢰⠇⣼⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠉⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠻⣄⠀⣰⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢀⣤⣶⣾⣿⣿⡿⢣⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⢦⡁⠼⠁⠀⠀⠀⠺⣿⣿⣶⣤⡀⠀⣸⣿⣿⣿⣿⣿⣿⡟⣱⣿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢙⢦⡙⢦⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢸⣿⣿⣿⡿⣫⣵⣶⠂⣿⣿⣿⣿⠿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠋⠀⠹⡄⢳⡄⠀⠀⠀⢰⣿⣿⣿⡿⢸⣿⣿⣿⣷⣬⣛⠻⠂⣿⣿⣿⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠶⠶⠖⢹⡄⢷⠀⠀⠴⠿⠿⠟⠋⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻⠶⠶⠶⠶⠶⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠙⣛⣿⣿⠿⠿⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉




⡶⢶⢶⢶⠶⠶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⠶⣶⠶⢶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⣿⣿⡿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡷⢟⣛⣛⣛⣛⡻⢾⣷⡄⢀⣤⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡵⢟⣛⣭⣭⣭⣭⣛⡳⢯⣿⡿⠽⠭⢭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⢞⣋⣭⣥⣶⣶⣬⣭⣙⣿⡿⠭⣍⡛⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢋⣭⣴⠶⠶⠶⠶⠶⣟⣓⣒⠒⢦⡉⠳⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣞⡯⣻⢿⣿⠇⠀⠐⣶⠶⠒⠛⠒⠲⠁⠢⢌⠑⢆⠙⢆⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠠⣑⠲⠶⠖⣛⣋⣭⠶⣚⡭⢞⢕⡣⡊⠀⠀⠀⠈⠛⠛⢛⣋⠀⢉⠑⡀⠡⠀⢣⠈⢧⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣙⣛⣋⣉⣥⠶⢚⣩⠖⣡⢊⠀⠀⠀⠀⠀⠀⠀⠉⣉⡁⠀⠀⠀⠀⠀⠡⠀⠂⠘⠘⢷
⠀⠀⠀⠀⠀⠀⡀⠀⢤⣉⣉⣉⣩⡤⠖⢋⡥⢚⡵⡡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⢧
⠀⠀⠀⠀⠀⠀⡇⠂⠀⠈⢉⣉⣠⡤⠞⢋⡴⢋⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣧
⠀⠀⠀⠀⠀⡀⡇⢸⡀⠋⠉⠉⢁⣠⠶⠋⡠⠋⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⡌⢧
⠀⠀⠀⠀⠀⡇⢹⡀⢧⠀⢠⠞⠋⠀⡠⠊⢀⠊⠀⠠⠠⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠹⡌⢧⡀
⠀⠀⠀⠀⠀⢹⡈⢧⡈⢧⠈⠀⢠⠞⠀⢠⠃⠀⠀⠀⢢⡈⠢⡈⢢⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⢣⠹⡌⢳⣄
⠀⠀⠀⠀⠀⠀⢳⡈⢷⡈⢳⡀⠘⠀⠀⡇⠀⠈⣁⠙⢦⡙⢦⡈⠢⡉⠂⠀⠀⠀⠀⠀⠀⡜⢀⠃⡰⠀⡜⢀⡖⠀⠀⢣⠹⣄⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠻⣄⠙⢦⡀⠀⠈⠀⢠⡈⠳⣄⡙⢦⣈⠲⣌⠲⠀⠀⠀⠀⠀⠘⢁⠎⢰⠃⣸⠁⡼⠁⡀⠈⡈⢆⠙⣦⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡘⢷⣌⠻⣦⡉⠳⣦⡙⠷⣌⠙⢦⣉⠳⣌⡓⠀⠀⠀⠀⠀⢀⠎⣰⠃⣰⠃⡼⠃⣴⠃⡄⠠⠈⢇⠈⢷⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⢷⣌⡙⢷⣌⠛⢦⣌⠛⢦⣌⠳⢦⣙⠃⠀⠀⠀⠀⠘⡔⢁⡼⢁⡼⢁⡼⠃⣰⠃⠀⢃⠈⣆⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣝⠻⣦⣙⠻⣦⣌⠻⢦⣍⡛⢶⣍⡛⠀⠀⠀⠀⠈⣴⠏⣠⠞⣠⡞⢁⡼⠁⣴⠇⠾⠀⢸⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⣙⠷⣦⣝⠻⢶⣬⣛⠷⣮⣍⡆⠀⠀⠀⠀⣤⠞⣡⡾⢋⣴⠏⣠⡞⢁⡼⠃⣀⠜⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣮⣝⡻⢶⣬⣝⡻⠶⣮⡅⠀⠀⠀⢘⡴⠞⣩⡴⠛⣡⡾⢋⣴⠟⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣮⣭⣛⣻⠶⢮⠀⠀⠀⢰⣞⣛⣩⡴⠟⣩⡴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢻⡀⠀⠀⢸⣭⣭⠴⠶⣛⣩⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⢀⠈⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠪⠼⡀⠀⠀⠀⠀⣴⣶⣄⠀⠀⡃⠀⠉⠀⠀⠀⠘⣌⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠅⠀⠀⢀⣿⠀⠙⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⢠⠀⠀⠀⠀⠀⠣⠀⠀⠀⡼⠼⣷⡄⠈⡷⢦⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⣠⣤⣼⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⡄⣧⠀⠰⠤⢘⣿⠿⣅⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣠⣤⡀
⡟⠉⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⢸⣷⠶⢿
⠁⠀⠀⡾⡁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣄⣠⣤⠀⠀⠐⠿⠷⠺⢆⠀⠀⠀⠀⠈⢳⠀⠈⠻⡄⠈
⠀⠀⠀⠔⠛⠀⡿⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⢆⡀⠀⠀⢤
⠀⠒⠀⠀⠀⠀⠀⠀⣤⣴⠿⠏⠈⠡⠁⠀⠀⠐⠦⣴⢶⣦⢤⣤⣀⣀⣠⡤⠤⠀⠀⠀⠹⠿⠛⠛⠇
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⣠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢜⢭⡻⢯⣤⣀⡀
⠀⠀⢱⣆⠐⠊⢁⡀⠀⠔⠀⠀⠀⡠⠀⠉⠢⠀⠀⠀⠀⠀⢀⡌⣇⠈⠛⠛⠿⠿⣿⣦⣄⢀⣠⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⡎⠀⠀⠀⠀⠀⠀⠈⢹⠋⠀⠀⠀⠀⠇
⢦⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠉⠀⠀⠀⠀⢆⠀⠀⠈⠀⣀⡤⠰⠶⣄
⡴⡞⢰⡀⢀⡠⠞⠁⣠⣤⣴⠒⠒⠞⠀⠀⠀⡁⠀⠀⠀⣴⣧⠈⠓⢆⡀⠀⠀⠈⣇⠀⡠⣄⠘⠉⠤⢤⡤
⠀⠇⠉⠉⠁⠀⠀⢸⡏⣵⠬⠉⣚⠋⠀⠀⠈⢰⡀⠀⠐⣓⡹⠄⠀⠀⠀⠀⠀⠀⠋⡴⣡⠈⠐⣇⡀⡰⠄
⠸⠁⠀⠀⠀⠀⠀⣸⣷⢿⣿⣿⣥⡰⡀⡀⠀⡄⢱⠀⠀⢱⠖⢛⡀⠀⠀⠀⠀⠀⢸⡛⠛⢶⡞⠀⢈⡧⢰
⠀⠀⠀⠀⠀⠀⠠⠏⢡⡎⢾⠈⢳⣭⣙⣋⣼⠁⠃⠀⠀⢸⡅⡄⠶⠀⠀⠀⠀⡴⠈⢉⣦⣰⣟⣀⠞⠉⠉
⢤⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⣏⡟⢿⡏⣴⠀⠀⠀⠘⢧⣔⠞⠁⠀⠀⠘⠀⠥⠈⠈⠉⠉⠋⠙⠛⠛
⠉⠁⢀⣤⡶⡟⠓⢦⠀⠃⠀⠀⣸⣿⠀⠀⢿⠁⠀⠀⠀⠀⢸⠅⡠⢄
⠀⠀⢸⠁⠁⠀⣠⣐⠆⠀⠀⢠⢿⡟⠠⣄⡾⠀⠀⠀⠀⠀⠀⠣⠿⠗⠀⠀⠀⠀⠀⢀⠴⠒⠒⠠⠄⣀
⣀⣀⣨⣪⣄⣀⣀⣈⣀⣀⣀⣀⣚⣀⣀⣀⣀⣀⣀⣀⣒⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣍⣀⣲⣂⣀⣀⣀⣷
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⢉⣀⣤⣤⡄⠀⠈⠉⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⣠⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠛⠻⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⡿⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠋⠉⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣤⣤⣤⣤⣶⣿⠿⢿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⣷⣦⣄⣀⠀⠉⠉⠀⣀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣋⡉⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠹⣿⣆⠀⠀⠀⢀⣾⡿⠛⣿⣧⠀⠀⠀⠀⠀⢀⡄⠀⢶⣿⣶⠆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠹⣿⣆⠀⠀⣾⣿⠁⠀⠘⣿⡇⠀⠀⠀⣬⣿⣧⡀⠀⣿⠁⠀⣸⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠙⣿⣧⠀⢻⣿⣤⣀⣴⣿⠇⠀⠀⣤⡀⠀⠈⠻⣦⣿⣠⡾⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⢾⡿⠶⠶⠶⣿⣿⣿⡷⠶⠶⢿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⡾⠋⣿⠉⠻⣦⡀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠀⠀⣿⡀⠀⢸⡿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠾⢿⠿⠆⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⠿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠛⠛⠿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢀⣠⣴⡶⠶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠾⠿⠿⠿⢶⣤⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⡾⠟⠋⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⢻⣧⣠⣤⣤⣤⣄⡀⠘⣿⡀
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠉⠙⠻⣷⣿⡇
⠀⢀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠉⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⢀⣤⡾⠟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡾⠋
⠀⣴⡿⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡆⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉
⠀⣿⡄⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡇
⠀⠙⠿⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢿⡇⠀⠀⠀⣠⣾⠟⠋⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠸⣿⡀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠉⠀⢸⡇⠀⠀⢰⣿⠁⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⣷⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⢸⣟⠀⠀⠀⠀⣿⠇⠀⠀⠘⣿⣄⣀⣠⣼⡟
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⣿⡇⠀⠘⢿⣦⣀⣠⣾⠟⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⣿⡇⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢿⣦⣄⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣄⠀⣀⡤⠴⠖⠒⠒⠒⠀⠭⢁⡀⠐⠒⠒⠰⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠓⠀⢀⡽⠉⡁⠀⠈⠁⠒⠠⢀⠀⠀⠀⠀⣉⡲⠶⠋⠁⡠⠚⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠅⠀⠈⠀⠀⠀⠀⠀⠀⣉⡢⢖⠉⠀⠀⠀⢀⠊⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠇⠰⣆⡀⠀⠀⠀⣠⠔⠚⠋⠢⢄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡂⠙⠆⡠⠊⢠⠖⠋⠉⠉⠢⣱⡀⡠⠴⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠃⠀⠀⠇⢠⢾⡁⢀⡎⠀⢀⠀⠄⣡⡔⡉⠀⠀⠑⢄⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⢀⠴⡏⢸⠀⠈⢇⡀⠉⠁⠠⠀⠢⡃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⡔⠁⠀⠀⠈⢇⠀⠈⢦⣀⣀⠛⠡⣤⠅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⡞⠀⠀⠀⠀⠀⡠⠛⡲⠫⠅⠒⢰⣮⠳⠦⢄⡀⠑⠦⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠎⠁⢀⠤⠔⠒⠎⢀⠞⠀⠀⠐⢶⡆⠘⣺⠊⠲⡁⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠘⡾⢀⠞⠁⡀⠀⠀⡠⠋⠀⠀⠀⠸⡜⠛⠉⠸⢁⣀⣹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠢⡴⠁⠀⡀⠀⠀⠁⡇⣀⠠⠜⠉⢆⠈⠪⡹⡂⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠞⠈⠢⡀⠑⣀⠀⠀⣥⠃⢀⠀⠀⠈⢧⠀⠑⢌⠻⢄⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠈⠀⠈⠁⠀⠘⠀⠀⠑⠀⠀⠈⢧⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡄⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠈⢧⠓⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠴⠤⢤⣀⣀⣀⣈⣁⣠⠤⠤⠤⠖⠒⠚⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡠⣦⠔⠊⠀⠀⣠⠁⠢⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡸⡄⠙⢄⣀⠔⠚⠁⠀⠀⠱⡀⠀⣀⠦⢠⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢴⠊⠀⠈⡢⠤⠛⢀⣀⠤⠀⠀⠒⠁⡎⣠⠔⠚⣇⣀⣤⡀⠠⠂⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⡀⠈⠳⡀⠈⠣⠀⠀⢠⡀⠀⠀⠀⠐⠀⠙⠣⣀⠀⣤⠋⢀⠞⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠑⠠⠔⠃⠀⠘⠀⠀⠒⢀⠀⠠⠀⠀⢸⡴⢛⡶⠁⢀⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⠶⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠉⠀⠈⠂⠴⠶⠉⠩⠐⠋

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠉⠑⢄⠀⢠⠒⠉⠑⢆⠀⠠⠠⣶⡆⠀⠀⠀⠀⠠⡀
⠀⠀⠛⠑⠒⠈⠁⢀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠄⠀⢈⠀⠸⡀⠀⢁⡜⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⠄⠘⠤⣀⣀⡠⠊⠀⠀⠈⠉⠉⠀⠀⠀⢀⠀⠀⠀⠐⠀⠈⠀⠄⠑
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⣠⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠁
⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠐⠦⠄
⠀⠀⠀⠐⠐⠁⠀⡀⠀⠀⣀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠆⠀⠃
⠀⠀⠀⢀⠀⠀⠘⠟⢄⠠⠛⠁⠀⠠⠀⠀⠀⠀⢀⠼⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠄
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠁⠈⣉⢿⡷⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⡃⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠶⠎⠛
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠑⠠⠂⠁⠀⠀⠀⠀⠈⢤⣀⣀⣄⣼⠗⠀⠀⠀⠀⣭⠑
⠀⠀⠀⠀⠀⠈⠛⠢⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠿⠸⡅⠁⠂⠈⢄⡀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢉⡉⠉⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡠⠖⠋⠉⠁⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⢤⡀
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⡛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⠇⠀⠀⠀⣰⠃⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠏⠀⠀⠀⠐⠃⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⢰⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⣀⡼⠀⠀⠉⠛⠉


⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢰⡂⡖⠲⣰⠐⡖⢰⡄⢰⡢⠀⠀⣖⡀⠠⡂⠐⡖⢰⡢⡴⠒⡄⣤⠂⣖
⣤⣤⣤⣤⣤⣤⣤⣤⣷⣼⣼⣤⣧⣯⣽⣴⣼⣴⣤⣧⣤⣤⣼⣤⣧⣬⣵⣵⣴⣥⣭⣦⣧⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠄⠀⠉⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⡀
⠠⠁⠀⠀⠀⠀⠀⣀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠲⣄⠀⠀⢀⡴⠊⠉⠓⢄⠀⠀⢀⠔⣡⣲⣆⠀⢠⠀⠁⠈⠀⢘
⠀⠈⢯⠇⣀⣀⠸⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠂⠖⢈⡇⢠⣁⠁⠈⠛⠃⠀⠈⠀⠠⠀⠄⠌⠓⠀⠠
⠐⡀⠀⠀⠈⠉⠀⠀⠀⣠⠄⠒⠀⠀⠢⠄⡀⠀⢸⡀⠀⠀⠉⠀⠀⢀⡏⠀⠘⢦⣀⣀⣠⠞⠀⠀⡤⠀⠀⠀⠀⡀⠀⢠⠀⠠⡀⠀⠀⢀⠲⠄⠠⠐⢈
⠀⠀⠠⢀⠀⠀⠀⠀⠘⡁⠀⠁⠀⠁⠀⢄⡈⠄⠀⠑⢤⣀⡀⣀⡠⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢄⡀⠠⠊⠀⠄⠨⠠⠈⠁⠀⡤⣀⣋⣁
⠀⠀⠀⠀⠀⠑⢀⠀⠀⠂⢈⠂⠀⠂⠔⠈⠑⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠘⠓⠛⠓⢃⠠⠈⠈⠀⠀⠀⠀⠈⠂⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡦⢉⠀⠀⠀⠐⠠⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠳⠠⠊⠈⠀⠊⢥⡀⠀⠀⠀⣀⡀⠐⠃⠀⠐⠄⣀⡀⠀⠀⠀⠀⠂⠀⠤⢀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠈⠂⠀⢆⠀⠀⣀⡀⠀⣀⡀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠑⠄⠉⠁⠐⠉⠁⠔⠀⠀⠀⠀⠐⠀⠀⠖⠐⡄⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⢀⠀⠀⢀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⣦⠀⣾⡶⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠊⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⢨⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⢥⠀⠀⡬⠐⢠⣉
⠀⠀⠀⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠈⠉⠀⡀⠊⠀⠈⠀⠠⠀⢎⢣
⠀⠀⠀⠀⠓⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠀⣀⡀⣶⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢠⠁⠐⠈⠃
⠀⠀⡠⠀⠐⠀⠀⠀⢿⡿⠀⠀⡘⢿⠇⠀⠀⢙⡂⢄⠀⠀⠀⠀⠀⣰⣿⠦⢀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡀⠊⢀⠠⢊⡘⠀⠀⠀⠀⢁⠂
⠀⠀⠈⠀⠊⡀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⡌⢋⠁⠀⠀⢀⠤⠜⠁⡽⢷⣦⣄⣁⣰⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⢀⠊⠱⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡁⠁⠀⢄⡀⠀⠀⠀⠀⠀⡀⠔⠢⡉⢎⠀⠀⠀⠀⠀⠀⠀⢀⡾⡻⣞⡅⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠃⠀⠀⠀⣰
⠀⠀⠀⠀⠑⠁⠀⠀⠀⡉⠀⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠘⠀⠇⠀⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⢄⠀⠀⠐⠀⠰⡀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⠀⠀⣶⣶⠀⠀⠠⠔⠆⠀⠀⠀⠄⠀⠰⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠰
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⣄⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠆⠀⠀⡀
⢆⠀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⠀⠀⠀⠀⢷⠟⣀⠀⡨⠛⠋⠀⠠⠀⠀⠁⠐⡄⠀⠀⠀⠀⠀⢒⣟⣴⠀⠀⠀⠀⠠⠔⠠⠄⠈⠆
⠀⡀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠓⡆⢶⢴⡲⣏⠎⠀⡢⠀⠀⢈⠀⣞⠓⣀⡀⠁
⠀⡡⠂⠀⠀⠀⠀⠈⠙⠣⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠅⢠⡝⡊⠿⡅⠀⠁⠀⠈⢅⢀⠈⠀⡈⠉⠉⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠈⠉⠉⠛⠛⠛⠛⠛⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠲⠠⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠤⣄⠀⣠⠖⠋⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠦⢄⡀
⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠳⢄⠀⣠⠴⠖⠒⠲⢤⡀⠀⠀⢠⠔⠚⠉⠙⠒⢤⠀⣀⠤⠶⠶⠿⣄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠙⢆⢰⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀
⠀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⠋
⠀⠈⠓⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡰⠃⠀⠳⣄⡀⠀⢀⣠⠔⠙⠢⢤⣄⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣠⠴⠊⠀⠑⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡤⣄⠀⠀⠀⠀⡴⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡴⠉⢦⠀⠀⠀⡼⠁⠘⡄⠀⠀⣸⠁⠀⢸⡄
⠀⠀⠀⢀⡴⡄⠀⠀⠀⠀⠀⠀⡼⠁⠈⣇⠀⠀⠀⠀⠀⡇⣹⠀⢰⠃⠀⠈⡇⠀⠀⠣⡀⣠⠇⠀⠀⢻⡀⠀⢠⠇
⠀⠀⠀⡞⠀⠸⡄⠀⢀⡀⠀⠀⡇⠀⠀⢸⠀⢀⡀⠀⠀⠈⠁⠀⠸⣄⡀⣠⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠚⠉
⠀⠀⠀⠳⣀⡴⠃⠀⣇⣳⠀⠀⠙⠦⠴⠋⣰⠋⢳⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣄⠀⠀⢸⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡄⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⠀⡰⢆⠀⠀⢠⠎⠈⢧⠀⠀⠉
⠀⠀⠀⠀⠀⡰⢲⡀⠀⠀⠀⡏⠘⡆⠀⠀⠈⠓⠋⠀⣠⠶⡄⠀⠰⡇⢸⠆⠀⢸⠀⠀⢸
⠀⠀⠀⠀⢰⠁⠀⢳⠀⠀⠀⠓⠖⠁⠀⠀⠀⠀⠀⢰⠇⠀⢹⡀⠀⠉⠉⠀⠀⠀⠑⠒⠋⠀⢀⣤
⠀⠀⠀⠀⠸⣄⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢠⠄⠐⠶⠀⠈⢈⡠⠊⠁⠀⠐⠃⠸⠃⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢟⠏⠉⠀⠈
⠀⠀⢰⢁⡾⠀⠀⠀⣀⡼⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⡔
⠀⠀⠈⠠⢤⣀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢠⠄⠁⠀⠶⠘⢲⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡤⠀⠀⠀⠶⠁⢀⡴⡁⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⣶⢶⢲⠒⡆
⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠐⡷⣮⡏⠿⠘⢰⠃⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣤⣴⡖⡖⡆⠀⠀⠀⠚⠳⠧⠆⠎
⠀⠀⠀⠾⠀⢠⠆⠀⠀⠰⣄⠀⢸⣴⡇⠀⠀⠀⠀⠤⠔⠀⠀⠀⢲⣾⡏⡇⠀⡇
⠀⠀⡀⠀⠰⠈⠀⠀⠀⠐⢂⢼⣿⣷⠯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⣰⡾⣠⠀⠀⠀⠀⡤⣡⠻⡟⠻⡕⠀⠀⠀⠀⢠⢿⣷⠀⣠⡤⣶⣶⡶⠀⠀⠀⣄⠒⣄⠀⢠⠀⠀⡆⠂
⢠⠀⠀⢐⣿⠁⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠩⠬⠱⡰⠉⠁⠀⠀⠀⠀⠈⠁⠘⢀
⢸⡄⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡽⣆⠁⠀⠀⠀⠑⣃⠀⠀⠀⠀⠀⠀⣀⡝⠀⠄⠀⣤
⠀⢳⡄⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢸⣿⠁⠝⠀⠠⠄⠀⠄⡑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠃
⠇⣺⡄⣾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠚⠃⠀⠈⠠⠢⠁⡀⠒⠬⣆⠀⠄⠀⠀⠀⠶⠄⠀⠁⠈
⣇⣟⣼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠸⠾⠛⠋⠈⠙⠀⣆⠀⠀⠀⠀⠀⡀
⠘⠋⠁⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⡇⠀⠀⠈⠢
⣤⠶⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠈⣆⠘⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠨⡇⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡯⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢆⣰⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⢀⠀⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⡃

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠔⠋⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⡀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠈⠀⢤⠀⣢⠠⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢐⡂⡆⢒⢢⣄⣀⠀⠀⢀⠔⡈⠐⠀⠘⠀⠀⢀⣴⠏⠑⠎⠉⠖⠓
⠀⠀⠀⠀⠠⠀⠉⠀⠤⠀⢀⠀⠐⡂⢱⠀⠀⠀⠀⠀⡀⠞⢿⣩⢝⡱⣣⣞⡴⡯⣯⢕⣷⣮⡄⠀⠀⢸⠀⠀⡮⠛⢄⠀⢡⢠⠀⢠⠆
⠀⠠⠏⠢⢀⡱⡀⠀⡀⢀⠀⢁⣈⡀⠌⠀⠀⠀⢀⠌⢰⣦⠈⣗⣩⢟⣳⣳⣯⣭⢽⣹⡟⠯⢁⠀⠀⢘⠄⠀⠳⣄⠀⠡⣌⣜⠀⠜
⠀⠀⠀⠈⠒⠞⣵⢃⠣⠘⡁⠂⢡⠀⠀⠀⠀⠀⠘⠽⠀⠀⠀⢹⣾⣿⣿⣾⢿⠭⠋⠁⠈⠐⠠⢁⣀⣠⠆⠀⠀⠀⠁⠂⠬⠥⠊
⠀⠀⠀⠀⢸⣠⠁⢸⠀⠁⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠖⠿⠛⠋
⠀⠀⠀⠀⠈⠁⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⢫⠥
⠀⠀⠀⠀⠀⢀⣤⠐⠖⠀⠐⠖⠀⢀⠀⠀⠀⠀⡀⡜⠡⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡼⣁⠁⠀⢸⢶⠁
⠀⠀⠀⠀⡼⡁⠀⠀⠑⠂⠀⣀⠀⠈⠓⢄⠀⠌⣀⣡⠷⡚⡀⠀⠀⠀⢀⣨⠛⡒⠤⢤⣡⡶⠢⢄⢣⠀⠀⠀⢈⡟⢠⡟⣦⣢
⠀⠀⠀⢰⠀⠀⠰⡟⣆⠀⠀⠀⠀⠠⠄⠀⠓⠀⢄⣀⠤⠃⢰⠀⠀⣠⣙⠆⢧⣤⠂⢨⢽⢃⡇⣼⡜⠀⠀⢠⠋⡀⠀⢿⢅⢨
⠀⠀⠀⠘⠀⠀⠀⢉⠁⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠎⠀⠀⠈⠢⠄⣦⣮⡶⠁⣬⣿⢫⠏⣰⡄⠀⠘⢄⢱⠀⢸⡟⠉
⠀⠀⠀⠀⠰⡖⠒⠉⠀⡠⡤⢖⠖⡲⡲⠲⢶⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠣⣣⡮⠚⠁⠀⢰⠲⢈⠇⣼
⠀⠀⠀⠀⠀⠈⠐⠐⠯⠮⠰⠅⠾⠚⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠚⠁⠀⠀⠀⠘⠦⠥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⡀⠀⠀⠀⢀⠎⣀⠀⡦⠀⡃
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠖⢂⠀⢀⣰⣤⣤⣀⡔⠉⡄⠔⣀⠀⠡⡂⠀⠀⠨⡀⠙⠀⠂⢔⢩⣴⡀
⠀⠀⠀⢃⠘⣢⠄⠐⣶⠀⠀⠀⠀⣴⡊⠀⠩⣥⠀⠒⠀⠐⠖⢒⣒⣻⣿⣾⣿⠤⠤⣀⠀⡴⠀⠀⠀⠈⠒⣀⠰⣞⠣⡙⢿⣦
⠀⠀⢀⠔⠲⢓⠄⠐⣇⠀⠀⠀⣌⠈⠋⠀⠀⠺⠀⠐⣊⣩⡭⢟⡻⠛⠁⠃⡅⠀⢄⠈⠠⠂⠀⠀⠀⠀⠈⠑⢄⠂⢹⣟⡿⣿⡷⣄
⠀⠀⠃⠄⠂⡀⣸⠂⠘⠀⠀⠀⠀⠐⠠⠀⣀⣘⡇⠩⠤⠐⠊⠁⠀⠀⠈⠁⢤⢘⠘⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣌⢮⡙⠊
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠓⠁

⠀⢀⠀⣀⠀⠀⠀⣠⣤⠀⠀⣠⡄⢀⣠⡀⠀⠀⡤⠠⠄⠀⠠⠀⢀⣠⣄⣀⡀⠀⠀⣀⣀⣀⡀
⠀⠸⠀⠉⡜⠀⠀⠙⠿⠃⠐⠿⠀⠐⠛⢋⣤⣤⣤⣶⣶⣤⣤⣄⣈⠙⠉⠉⠁⠀⠻⢿⣿⣿⡿⠂
⠀⢠⠠⠊⠀⠴⢶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠁⣀⣀⠀⠀⠀⠀⡀⠄⠀⢸⢰⢺⡇
⠀⡄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠘⠿⣿⣿⣿⣿⣿⡿⡛⠛⠛⠛⠛⢻⣿⠛⠁⠀⢤⢠⣿⠇⠀⠀⠈⠈⠈⠁
⠀⠈⠑⠀⠀⣾⣖⠀⠀⢠⣤⠀⠀⠉⠉⠀⠀⠀⢡⠄⠀⣀⠀⠀⢠⣶⣆⠀⠈⠻⠀⠀⠀⠈⠛⠀⠀⠀⠀⣶⢠⡄⡆
⠀⢰⣿⣷⡄⠙⠇⠀⠀⠘⠋⢠⠀⠀⢠⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠉⠁⢠⣴⡶⠿⡇⠀⠀⠀⠀⣍⡀⠀⠛⠘⠃⠃
⠀⠘⣿⠀⠀⠀⠀⠘⠃⠀⡀⢸⡇⠀⠈⠉⠡⢠⢀⣤⢠⠉⠉⠀⡤⠀⢀⠘⠻⢷⣦⡇⠀⠀⠀⢸⣿⠄⠀⢠⢀⣀⡄
⠀⠀⣿⠀⠀⠀⠀⢸⣦⠀⣿⢸⣷⠀⠑⠀⠀⠀⠄⠀⠀⠀⢀⠠⠈⠀⠈⣀⣀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⢸⠸⠯⡇
⠀⠂⠻⠤⢝⣤⡄⠀⣿⣆⣿⣿⡿⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⢿⡇⠀⠐⠄⠀⠀⢰⡀
⠀⠘⢷⣲⣼⡽⠀⠀⠈⠿⣿⠟⢁⣀⡈⠉⠀⠀⡆⢰⢶⡶⠂⠀⠀⡄⠈⠀⠀⠀⣰⣿⣿⣿⣦⠀⣳⠀⠀⢸⣶⣴⡇
⠀⠀⠀⠉⣿⣇⠀⠐⠀⢀⣴⣾⣿⡟⠓⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠰⣿⡄⠀⠈⠈⠉⠁
⠀⠠⡀⠀⣿⣿⣿⣶⣶⣿⣿⣿⣿⠃⠀⠀⢰⣿⣷⡄⠐⠐⠄⠀⠄⠀⠀⠀⠀⣀⣸⣿⣿⣿⣥⣄⢼⠃⠀⢀⢤⣤⡆
⠀⠀⠀⠀⠘⣿⠿⡿⢛⡉⠿⠛⠁⠀⠄⠀⠀⠉⣿⣷⣄⠂⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⢿⠿⣿⢻⡆⢀⠀⠰⠛⠹⠇
⠀⠀⠀⣶⣤⠈⠓⠁⠋⡀⠀⠀⣴⠀⠘⡶⠀⠸⠏⢹⡏⠀⠀⣿⠘⣿⡄⠙⢛⣱⢇⡇⣿⢸⣇⡀⠛⠋

⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⢠⡀⠀⢶⡀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⢙⡆⠀⠀⠐⠿⠀⠀⠸⡆⠀⠀⢸⡆⠀⠉⠀⠀⠀⠀⠸⠆⠀⠈⠀⠀⢰⣇⠀⠘⠞⠀⠀⠀⢸⡆⠀⠀⠀⠀⢣⡖⠀⠀⠀⠀⣷⠀⠀⠀⣘⣃
⠘⠁⡟⡄⠀⠀⢀⠀⠘⠇⠀⠀⠘⠃⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡶⡀⠘⠃⠀⠀⣀⠀⠀⠀⠀⢰⢣⠀⠉⠀⠀⠀⠘⠋
⠀⠀⠙⠁⠀⠀⣹⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⢀⢙⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⡀⠀⠀⢠⢇
⢀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣭⡄⠀⠀⠀⡀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⢰⠆⠀⠀⣥⠀⠀⠈⠿
⢨⡇⠀⠀⣾⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠈⠾⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠀⠘⠃⠀⠀⠉⠀⠀⠀⣤
⠈⠁⠀⠀⠙⠃⠀⠠⣿⡀⠀⠀⣿⡄⠀⠀⠉⠀⠀⠀⠀⢀⣀⣀⣀⣘⣿⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⢀⡀⠀⢀⡀⠀⠛⠁⠀⠀⠈⢀⡠⠤⣴⠶⣲⠆⣉⠥⣒⠨⠄⠂⠉⢏⠉⣍⠒⠒⠲⠦⢤⣤⣀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠺
⠀⠀⢸⣽⠀⠸⠇⠀⠀⣀⣤⣖⠉⣡⢔⡯⠒⡩⣖⠭⢒⡩⠄⠂⠀⠀⠀⠎⠎⢒⠉⠄⣀⠀⠀⠀⠉⠛⠯⣭⣑⠒⠲⠤⣄⣀⠀⠀⠀⠿⠃⠀⠲⠃
⢀⡀⠀⠛⠀⠀⢀⡔⠚⠽⠂⢀⠞⢓⠥⣪⠕⣪⠔⣊⡥⠒⠀⠀⠀⠀⠀⠠⠸⡀⠯⣐⢀⠈⠐⠀⠀⠀⠀⠰⠙⢯⣔⠖⠀⠈⠙⠲⣤⡀⠀⠀⠀⣴⡀
⢨⡇⠀⠀⡠⠞⡁⠚⠁⠀⢠⠏⢊⠕⣪⠔⣫⠔⣪⠵⠚⠀⠀⠀⠀⠀⠀⠀⠀⢇⠨⢃⡀⠄⠀⠒⡀⠀⠀⠀⠀⠰⠙⣮⠔⣈⠥⢀⠀⠉⠲⣄⠀⠻⠃
⠀⠁⣠⠚⡐⠭⠀⠀⠀⢀⡯⢐⡵⢊⠔⣪⢔⠩⢒⠨⠄⠀⠀⠀⠀⠀⠀⠀⠄⢸⢈⡥⢒⠨⠥⠀⠐⠂⠀⠀⠀⠀⠠⠌⢯⠔⡨⠄⢒⡀⠀⢈⢧⡀
⠀⡔⣡⢱⡦⠛⢄⡀⠀⢸⠔⡣⢚⢕⡽⢊⠅⢊⠥⢒⡩⠀⢀⠀⠀⠀⠀⠀⡀⠸⢘⠩⠔⣒⠨⠭⢄⣀⣀⡀⠀⠀⠀⠐⡀⢯⠔⣈⠄⢒⠠⠄⢳⠱⡄
⣼⠋⠉⠉⠉⠉⠑⠪⢄⡇⢪⣖⡴⠥⠞⠓⠚⠋⠚⠛⠒⠛⠲⠮⣴⣠⠄⠀⠀⠀⡅⣂⠥⣒⣬⣝⣒⣖⣀⣉⣐⣂⣀⠤⠶⡈⣏⣴⡮⠑⠂⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠳⢦⡀⣯⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣽⠀⠀⠀⢸⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢽⡀⠀⠀⡜⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡉⠛⠋⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⡠⢀⡠⢀⠠⢀⠤⢀⠤⢀⠠⢀⡠⢀⠀⣀⠀⡀⢀⡀⣀⠀⡀⠀⡀⢀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠉⠁⠐⠁⠚⠁⠊⠡⠖⠡⠔⠡⠔⢡⠔⡡⢊⡤⣊⠔⡩⠚⡡⢊⡠⣪⢔⡡⢊⠔⣉⠔⡩⢞⡤⣊⠔⡡⢂⠔⡠⢂⠴⣂⠔⡠⢂⡤⣠⠆⡀⣠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠐⠦⠰⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠠⠀⠀⠈⠁⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠁⠀⣛⠀⠩⠤⠐⠒⠃⣄⠀⠂⠈⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠅⠀⠈⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠀⠡⠄
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⡁⠀⠀⠀⠂⠀⠀⠊⢢⠄⠀⠀⠤⠤⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠄⠐⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⣉⠤
⠀⠀⠀⠀⠀⠀⡀⠈⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⡀⠀⢧⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠁⠀⠠⢐⠆⠐⠄⡀
⠀⠀⠀⠀⠠⡮⡉⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠄⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢴⣆⢨⠄
⠀⠀⠀⠀⡂⠀⠁⠐⠐⠃⠠⠈⡁⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠷⠼⠣⠄
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠋⠀⡘⠄⠀⠀⠀⠀⠀⢊⠂⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠀⠀⠅⢀⡀
⠀⠀⠀⢨⠆⠀⠄⠐⠔⢶⠀⡔⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠂⡠⠁⠀⠀⣀⣀
⠀⠀⠆⠈⢢⢀⠀⢀⡠⢌⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠑⣀⠆⠀⠈⠀⠀⠀⠊⢀⠄⠒⠀⠈⠀⠐⠢⠀⠀⠀⢄⠀⡢⠆⠀⠀⠀⠀⠀⠀⢟⠄⠀⠀⠀⠀⡌⠀⣤⡀⠀⠀⠀⢀⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠁⡣⠀⠁⠀⢀⢀⠀⣉⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠒⠁⢀⣘⠇⠀⠀⠀⠀⠀⠀⠀⡸⡄⢡⠢⠆⠶⣤⡄⡇⠀⠀⠀⠀⠀⠀⠏⠖⢲⠘⠇⠀⢂⢱⡀⠋⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡃⡥⠋⢀⠀⣿⢃⠁⠰
⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠔⠻⢪⢰⡜⡐⡄⢺⡁⠏⠇⠤⢁⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⡀⢩⡦⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡜⠁⡆⡀⢘⢂⠂⠈⠰⡀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠎⢀⢈⠀⣼⢿⠁⠀⠀⡄⢉⣀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠾⠫⢜⣃⣖⢲⠄⠀⠀⠀⠀⡝⢨⠑⠏⠄⣠⠂⠈⠀⠀⠀⠀⡀
⠀⠴⣅⣌⠀⠀⠈⢠⠟⠃⠀⠀⠛⠀⢰⠀⢀⢆⣠⡄⠀⠀⠀⠀⠀⠠⠠⠶⠩⢍⡉⠲⡀⡶⠃⠀⠀⢀⠀⠃⠸⡠⠀⢶⠁⡄⠶⠀⡀
⠀⠀⠈⠻⠷⠤⠖⢠⣖⡆⠀⠀⠃⠀⠀⢉⣴⠏⠨⠔⠒⠒⠀⠀⢶⣳⡨⠡⠑⢄⠈⣆⠆⠀⠀⠀⠀⠀⠀⠈⠄⢘⠃⠐⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠈⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠸⠿⠛⠿⠂⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⣻⣶⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⠀⠀⠀⠀⠑⠓⠀⠀⠀⠀⢸
⠛⡻⠀⠀⠀⠀⣀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣠⣴⡄⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⣵⣠⣶⣶⡶⢶⣖⠒⠀⠀⠀⠀⠀⠐⠛⠀⠺⠿⠿⠀⠀⠀⠀⠀⡏⡀⠀⠠⣧⣷⣾⣷⣾⢿⠇
⠀⠀⠰⠶⡀⠳⣿⣜⢿⣛⠛⢛⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⣼⣿⠿⣟⡆
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣳⠫⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣄⡀⠀⠀⠀⠀⠘⣯⣾⡿⠁
⡀⠀⠀⠀⠀⠀⠣⡘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⣠⡴⠾⠟⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⣾⠆⠀⠀⠀⢰⣶⣶
⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠈⣠⠀⣄⠄⠄⠀⠀⠀⡟⠉⠀⠀⠘⠃⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠠⢤⣀⣄⣠⠎⣽⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠑⢤⣀⢹⣷⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⣀⣀⣀⣺⠩⠁⣀⣬⣤⣤⣒⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠙⠛⢷⣿⡟⠢⠀⠀⠀⡀⢀⣿⣿⣶⡎⣀⠀⢈⣀⣠⣤⣴⡿⣽⣿⢾⡷⣷⡷⠟⢿⣿⣿⣿⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⡀⠀⠀⢀⣤⣾⣿⣿⣷⣿⣶⣿⣿⣛⣿⢿⣟⠿⣯⡭⠾⠃⠀⠀⠈⠙⢻⡿⠟⠉
⣤⣄⣤⣴⣆⠀⠀⠀⠀⠀⠰⠝⠿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠁⠐⠀⣠⠬⠟⠚⡻⠟⠀⠀⠀⢀⡠⠔⠋⠁⠀⢀⣀
⠉⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⣽⣿⣀⡀⡠⠄⠒⠀⠠⠽⠖⣚⣋⣉⠠⠄⠀⠶⠿⡿⠿⠂⠀⠀⠀⠛⠛⠃
⠀⠹⣿⠏⠀⠀⠰⠶⠶⠀⠀⠀⠀⣠⠒⠛⣿⣿⠋⠐⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠬⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠟⠛⡉⠉⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⢀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣾⣛⣿⡿⠂⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣶⣶⣭⣵⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠄
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠟⠯⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⢀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠃⢈⣿⡷⠂
⠿⠟⠛⠒⠤⠀⠀⢸⡁⡠⠄⠀⠀⢠⣶⣴⣤⣷⠄⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢺⠟⠛⠁⠀⢺⠟⠁⠀⠀⢰⠤⠤⠴
⠀⠐⠂⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠀⢸⣿⣿⡆⠀⠀⢀⡀⢠⣶⣾⣿⣯⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⢀⣠⢄⣀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠁⠀⠿⣷⣷⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠊⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⡀⠀⡀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡠⠘⠂⠉⠐⢀
⠀⠀⠀⢀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠑⠀⠀⢀⠤⢄⣠⠤⢄⡔
⠀⢀⠊⢀⡈⠀⠀⠀⠄⢀⡄⠄⠒⢒⠹⠛⡛⠛⠛⠔⣛⠠⠄⡀⠁⠀⠀⠁
⠀⠀⠒⠒⠒⠀⠀⠒⠂⠀⠀⠀⠔⠁⠀⠀⠈⡄⠀⠀⠀⠉⠢⡀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠈⠈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠐⢅⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠄⢀⠀⠤⠄⠀⠄⠈⢣⡀⠄⠂⠉⠉⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠀⠀⠀⠀⠴⠐⠀⠉⠄⠋⠀⠀⠈⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⢀⢀⢂⠀⠀⠀⠀⠠⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⣿⠐⠐⢒⠀⢀⠀⢀⠀⠒⢒⠒⠒⠒⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡖⢀⠀⣽⠀⠀⠎⢀⡍⠀⠄⠀⢀⡍⠀⡀⠁⠠⠏⠀⠌⡔⠰⠁⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠆⠀⢠⠀⢀⠃⠀⢀⡂⠸⠁⢀⠄⠀⣐⠀⡴⠀⠠⠆⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠀⠀⡼⡀⠈⠀⢀⠈⠀⠀⠀⠘⠠⠀⠁⠀⣠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠃⠀⡼⠀⠎⠀⠋⢀⠆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠊
⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⡂⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁